If you wish to use an older version that will work (not recommended due to security issues) you can follow these steps, assuming you still have java 6 installed: http://support.apple.com/kb/HT5559 (summarised below)

Hit enter and if java is not installed you'll get a message that reads "No Java runtime present, requesting install" followed by an alert requesting you to install java runtime. Click "install" to install the latest version of Java for your device.

Whilst your answer may theoretically answer the question, it would be preferable to include the essential parts of the article in an answer below, and provide the link for reference
–
PfitzNov 29 '12 at 10:12

"This release is for OS X Lion versions 10.7 or later." might also mean 10.7.0 up to 10.7.x. In any case, I couldn't use Java applications after running that installer and had to install the JRE from the Software Update dialog.
–
ؘؘؘؘAug 4 '12 at 14:48